Cabinet minister Uma Bharti has also offered to resign.
Bharti, who is the water resources minister, said only Shah or anyone on his behalf can speak on the issue.
"The media sought my reaction on reports in circulation since yesterday. I have said that I have not heard the question, will not hear nor will I answer it," she tweeted.
Rudy said BJP president Amit Shah conveyed him the decision that he should step down as minister.
Balyan said he was asked to resign and he did so immediately.
He said he would work to further strengthen the BJP in western UP.
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